Leaky Utility Sink / Odd Setup for Washer

I have a strange, leaky setup in my laundry room that I would like to repair and update. Looking for advice on the best way to address it. Here is my setup: There is a hot and cold line running out of the wall, with pipes running from them directly to a leaky old faucet. The faucet is attached to my utility sink. Also running from the hot and cold lines is a second set of pipes that have shut off valves and lines running to my washing machine. To make this a little more complicated, my washing machine drains into the utility sink. The pipes and handles for the washing machine are directly above the faucet, which (a) makes it hard to access the faucet and (b) causes confusion as to which handle to turn when turning on the water for the sink. Is there a standard setup that I could follow when I replace all of the old piping and leaky items? See attached photo. Thank you!

That is quite a configuation you have there, and it looks like you have copper pipe requiring soldering. You will likely have to pull the sink for a bit and open the wall to do the work (or to have it done professionally), but I would have new washer spigots recessed into the wall, and I would supply a new sink faucet from below.

For the washer, you might want to consider the newer style valve that shuts off both hot and cold with a single lever plug. This is a unit that sets in the wall, and if you can connect a 2" pipe and trap to your drain, the washer can drain through this also. A new faucet for the sink is definitely in order. I would agree that you probably will find cutting out drywall to access the pipes will be the easiest and quickest way to attack the problem.